Stability-Preserving Model Reduction and Interpolation for Vibration Optimization in Beam-like Structures

High-fidelity finite element models offer precise vibration analysis. However, their use in iterative optimization is computationally demanding. To overcome this, a stability-preserving framework for parametric model reduction and interpolation is developed. The interpolation approach is based on geometrically interpolating the poles of a system. As the scalar parameter varies, the poles follow specific trajectories, but their samples are only known at discrete points. Since the exact paths between these samples are unknown, a set of artificial trajectories is proposed. It is demonstrated that this set of trajectories guarantees stability and a bounded deviation in the H-infinite sense for multi-input multi-output linear time-invariant systems. Furthermore, all the trajectories that satisfy this bound are identified and presented. This approach introduces a new sampling criterion that assesses the parameter space sampling given on second-order models. In order to apply this criterion, a practical model order reduction strategy tailored to Bernoulli beam dynamics is presented. A numerical case study on a cantilever beam demonstrates the model order reduction method.